75x^2+50x=100

Solution for 75x^2+50x=100 equation:

75x^2+50x=100

We move all terms to the left:

75x^2+50x-(100)=0

a = 75; b = 50; c = -100;
Δ = b2-4ac
Δ = 502-4·75·(-100)
Δ = 32500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32500}=\sqrt{2500*13}=\sqrt{2500}*\sqrt{13}=50\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50\sqrt{13}}{2*75}=\frac{-50-50\sqrt{13}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50\sqrt{13}}{2*75}=\frac{-50+50\sqrt{13}}{150}
$